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Based on the magnetar model, we have studied in detail the processes ofneutrino cooling of an electron--positron plasma generating an SGR giant flareand the influence of the magnetar magnetic field on these processes.Electron--positron pair annihilation and synchrotron neutrino emission areshown to make a dominant contribution to the neutrino emissivity of such aplasma. We have calculated the neutrino energy losses from a plasma-filledregion at the long tail stage of the SGR 0526--66, SGR 1806--20, and SGR1900+14 giant flares. This plasma can emit the energy observed in an SGR giantflare only in the presence of a strong magnetic field suppressing its neutrinoenergy losses. We have obtained a lower bound on the magnetic field strengthand showed this value to be higher than the upper limit following from anestimate of the magnetic dipole losses for the magnetars being analyzed in awide range of magnetar model parameters. Thus, it is problematic to explain theobserved energy release at the long tail stage of an SGR giant flare in termsof the magnetar model.

Lower Bound on the Magnetic Field Strength of a Magnetar from Analysis of SGR Giant Flares